What is the law of detachment in geometry?

The law of detachment in geometry is a deductive reasoning principle that states if a conditional statement is true and its hypothesis is true, then its conclusion is also true. In other words, if "If p, then q" is true and p is true, then q must also be true. This law is commonly used in geometric proofs to draw logical conclusions based on given information.

For example, if the conditional statement is "If an angle is a right angle, then it measures 90 degrees" and it is given that angle A is a right angle, then we can conclude that angle A measures 90 degrees using the law of detachment.

It is important to note that the law of detachment only works in one direction, from hypothesis to conclusion, and does not guarantee the truth of the original statement. It is a fundamental principle in logical reasoning and helps to establish the validity of geometric arguments and proofs.